The dispute is the culmination of a long-running debate dating back to 2004, when 45% of DIS's shareholders answered a call from late Roy E. Disney and cast a vote of no confidence in the then-Chairman and CEO Michael Eisner.

Following that contentious period, the decision to revert back to having one person fill both roles was always going to ruffle a few feathers.

“The board concluded that succession planning would be best served ... by naming a successor CEO during Mr. Iger's extended tenure in order to enable a healthy mentoring process during the remainder of his term as chairman,” Disney wrote Thursday in a letter sent to shareholders explaining the decision.

However, the ISS said that, “The board's reversal of its prior commitment to an independent chair, without suitable transparency and input from shareholders, constitutes a material failure of governance.”